20_InstSolManual_PC - ELECTRIC CHARGE FORCE AND FIELD E...

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Unformatted text preview: ELECTRIC CHARGE, FORCE, AND FIELD E XERCISES Section 20.1 Electric Charge 14. Nearly all of the mass of an atom is in its nucleus, and about one half of the nuclear mass of the light elements in living matter (H, O, N, and C) is protons. Thus, the number of protons in a 65 kg average-sized person is approximately 27 28 1 2 (65 kg)/(1.67 10 kg) 2 10 ,- × × < which is also the number of electrons, since an average person is electrically neutral. If there were a charge imbalance of 9 proton electron | | 10 , q q e-- = a person’s net charge would be about 28 9 19 2 10 10 1.6 10 C 3.2 C,-- ± × × × × = ± or several coulombs (huge by ordinary standards). 15. I NTERPRET This problem deals with quantity of charge in a typical lightning flash. We want to express the quantity in terms of elementary charge e . D EVELOP Since the magnitude of elementary charge e is 19 1.6 10 C, e- = × the number of electrons involved is given by / . Q e E VALUATE Substituting the values given in the problem statement, we find the number to be 20 19 25 C / 1.56 10 1.6 10 C N Q e- = = = × × A SSESS Since 1 coulomb is about 18 6.25 10 × elementary charges, our result has the right order of magnitude. 16. (a) The proton’s charge is 2 2 1 3 3 3 1 , e e e e = +- corresponding to a combination of uud quarks; (b) for neutrons, = 2 1 1 3 3 3-- corresponds to udd . (See Chapter 39, or Chapter 45 in the extended version of the text.) Section 20.2 Coulomb’s Law 17. I NTERPRET In this problem we are asked to compare the gravitational and electrical forces between a proton and an electron. D EVELOP The gravitational force and the electrostatic force between a proton and an electron separated by a distance r are, respectively, grav 2 p e Gm m F r = and 2 elec 2 ke F r = E VALUATE The ratio of the two forces is 2 2 9 2 2 19 2 elec 2 11 2 2 27 31 grav 39 (9 10 N m /C )(1.6 10 C) (6.67 10 N m /kg )(1.67 10 kg)(9.11 10 kg) 2.3 10 p e F ke r F Gm m r---- × ⋅ × = = × ⋅ × × ≈ × Note that the spatial dependence of both forces is the same, and cancels out. A SSESS At all distances (for which the particles can be regarded as classical point charges), the Coulomb force is about 40 10 times stronger than the gravitational force. 20.1 20 20.2 Chapter 20 18. 52.9 a = pm is called the Bohr radius. For a proton and electron separated by a Bohr radius, 2 2 Coulomb / F ke a = . 9 2 2 19 11 2 8 (9 10 N m /C )(1.6 10 C/5.29 10 m) 8.23 10 N.--- × ⋅ × × = × 19. I NTERPRET This problem is about comparing the gravitational and electrical forces. D EVELOP The electric force between a proton and an electron has magnitude 2 2 elec / , F ke r = while the weight of an electron is ....
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20_InstSolManual_PC - ELECTRIC CHARGE FORCE AND FIELD E...

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